| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
|
| Initial Amendment Date: | February 24, 2021 |
| Latest Amendment Date: | June 18, 2024 |
| Award Number: | 2101800 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Andrew Pollington
adpollin@nsf.gov (703)292-4878 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2021 |
| End Date: | August 31, 2025 (Estimated) |
| Total Intended Award Amount: | $412,334.00 |
| Total Awarded Amount to Date: | $412,334.00 |
| Funds Obligated to Date: |
FY 2022 = $99,165.00 FY 2023 = $114,375.00 FY 2024 = $115,493.00 |
| History of Investigator: |
|
| Recipient Sponsored Research Office: |
201 PRESIDENTS CIR SALT LAKE CITY UT US 84112-9049 (801)581-6903 |
| Sponsor Congressional District: |
|
| Primary Place of Performance: |
155 S 1400 E RM 233 SALT LAKE CITY UT US 84112-0090 |
| Primary Place of
Performance Congressional District: |
|
| Unique Entity Identifier (UEI): |
|
| Parent UEI: |
|
| NSF Program(s): | ALGEBRA,NUMBER THEORY,AND COM |
| Primary Program Source: |
01002223DB NSF RESEARCH & RELATED ACTIVIT 01002324DB NSF RESEARCH & RELATED ACTIVIT 01002425DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
|
| Program Element Code(s): |
|
| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
This research project brings together different perspectives on singularities in commutative algebra and algebraic geometry. Both algebraic geometry and commutative algebra concern shapes defined by polynomial equations, such as the parabola that is the graph of the equation y = x^2. Not every shape is so smooth; some, such as the graph of the equation y^2 = x^3, have sharp points or other singularities. Study of geometric singularities is important in mathematics and has application to mathematical models for a wide range of important physical, social, and economic systems. Researchers have long known that important types of singularities in classical geometric settings also appear naturally when studying geometric shapes in modular (or clock) arithmetic. In fact, algebraic geometry in the clock arithmetic setting is a key component of modern communications infrastructure. This project aims to develop a theory of singularities in mixed characteristic, a middle ground between the classical and clock arithmetic worlds (that possesses aspects of both). The project also aims to develop geometric applications of this theory and to develop open-source software to study singularities in commutative algebra and algebraic geometry.
Techniques developed in number theory and arithmetic geometry have given rise to numerous recent breakthrough results in mixed characteristic commutative algebra. This project aims to use these methods to develop a singularity theory suitable for studying higher dimensional birational algebraic geometry in mixed characteristic, which would also facilitate translating many of the successes of positive characteristic commutative algebra to this setting. The project additionally aims to develop an analog of F-pure or log canonical singularities (and their centers) in mixed characteristic, to study fundamental groups of singularities, and to study boundary divisors in this setting.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
Note:
When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external
site maintained by the publisher. Some full text articles may not yet be available without a
charge during the embargo (administrative interval).
Some links on this page may take you to non-federal websites. Their policies may differ from
this site.
Please report errors in award information by writing to: awardsearch@nsf.gov.
